Optimal. Leaf size=38 \[ \frac{c^3 (a-b x)^5}{5 b}-\frac{a c^3 (a-b x)^4}{2 b} \]
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Rubi [A] time = 0.0390046, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{c^3 (a-b x)^5}{5 b}-\frac{a c^3 (a-b x)^4}{2 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)*(a*c - b*c*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 17.1044, size = 27, normalized size = 0.71 \[ - \frac{a c^{3} \left (a - b x\right )^{4}}{2 b} + \frac{c^{3} \left (a - b x\right )^{5}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**3,x)
[Out]
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Mathematica [A] time = 0.00307152, size = 40, normalized size = 1.05 \[ c^3 \left (a^4 x-a^3 b x^2+\frac{1}{2} a b^3 x^4-\frac{1}{5} b^4 x^5\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)*(a*c - b*c*x)^3,x]
[Out]
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Maple [A] time = 0., size = 45, normalized size = 1.2 \[ -{\frac{{b}^{4}{c}^{3}{x}^{5}}{5}}+{\frac{a{b}^{3}{c}^{3}{x}^{4}}{2}}-{a}^{3}{c}^{3}b{x}^{2}+{a}^{4}{c}^{3}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^3,x)
[Out]
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Maxima [A] time = 1.34954, size = 59, normalized size = 1.55 \[ -\frac{1}{5} \, b^{4} c^{3} x^{5} + \frac{1}{2} \, a b^{3} c^{3} x^{4} - a^{3} b c^{3} x^{2} + a^{4} c^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.181779, size = 1, normalized size = 0.03 \[ -\frac{1}{5} x^{5} c^{3} b^{4} + \frac{1}{2} x^{4} c^{3} b^{3} a - x^{2} c^{3} b a^{3} + x c^{3} a^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.066993, size = 44, normalized size = 1.16 \[ a^{4} c^{3} x - a^{3} b c^{3} x^{2} + \frac{a b^{3} c^{3} x^{4}}{2} - \frac{b^{4} c^{3} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.247579, size = 59, normalized size = 1.55 \[ -\frac{1}{5} \, b^{4} c^{3} x^{5} + \frac{1}{2} \, a b^{3} c^{3} x^{4} - a^{3} b c^{3} x^{2} + a^{4} c^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a),x, algorithm="giac")
[Out]